The default behavior seems to be that the app starts in all activities. I don't like that. I would rather prefer that the applications start only in the current activity.
Is there any configuration to do this?

Please provide details about your system, such which versions of the OS, Qt, KDE frameworks and Plasma you are using. (you can find this out by using the KInfoCenter app).

From my experience first with Plasma 4 on Ubuntu 14.04, now with Plasma 5.12.7 on Ubuntu 18.04 (KF5 5.47.0, Qt 5.9.5) is that application windows start on the activity they were launched in. There may be some exceptions depending on the application and how well it respects the window manager positioning, but I've only run into troubles there with certain apps like Chrome and Firefox, or GTK 3 apps when they are set up to use their own title bars instead of the system title bars.

That said, I've seen a couple other forum posts by people complaining about this same issue.

airdrik wrote:I've only run into troubles there with certain apps like Chrome and Firefox, or GTK 3 apps when they are set up to use their own title bars instead of the system title bars.

It seems like that is the issue. Most apps specially kde apps start properly but sometimes firefox starts on all activity. Most of times it is fine though.

The same issue with Vivaldi. Fortunately, you can set the native title bar which solves the problem.

After the last Google Chrome update it started to launch in all activities. All previous versions were opening in the current one.
Does anybody face this too? is it possible to solve this issue?

In my case Firefox started in just current and I wanted in all. That can be changed either way with a window rule, like here: https://unix.stackexchange.com/a/721739/341192